Tag Archives: fundamental subspaces

Linear Algebra and Its Applications, Exercise 3.4.15

Posted on December 28, 2017 by hecker

Exercise 3.4.15. Given the matrix find the orthonormal vectors and that span the column space of . Next find the vector that completes the orthonormal set, and describe the subspace of of which is an element. Finally, for find the … Continue reading →

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Linear Algebra and Its Applications, Review Exercise 2.27

Posted on January 4, 2014 by hecker

Review exercise 2.27. Find bases for each of the following matrices: Answer: If we put in echelon form (by exchanging rows 3 and 4) the resulting matrix would have pivots in columns 1, 2, and 4. Columns 1, 2, and … Continue reading →

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Linear Algebra and Its Applications, Exercise 2.4.3

Posted on April 30, 2012 by hecker

Exercise 2.4.3. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: We first consider the column spaces and . The matrix has two pivots and therefore rank ; … Continue reading →

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Linear Algebra and Its Applications, Exercise 2.4.2

Posted on April 23, 2012 by hecker

Exercise 2.4.2. For each of the two matrices below give the dimension and find a basis for each of their four subspaces: Answer: The echelon matrix has only a single pivot, in the second column. As discussed on page 93, … Continue reading →

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